The interplay of material transport kinetics and singular features associated with facets on surfaces leads to evolution behavior that is remarkably different from that of unfaceted surfaces. Alloy surfaces, in particular, demonstrate rich dynamics arising from the strong coupling of composition to morphology. The initial stages of relaxation of an unfaceted alloy surface are marked by kinetic decomposition of the alloy at the surface due to differing mobilities of the constituent species -at long relaxation times the surface returns to the equilibrium composition. In stark contrast, a faceted alloy surface undergoes kinetic decomposition and stays permanently locked at a non-equilibrium profile throughout relaxation. We present numerical simulations that demonstrate this unexpected behavior and provide an analytical model that elucidates the underlying physics. We show that the extent of kinetic segregation varies inversely with feature size and directly with the difference in diffusivities of the alloy constituents. Additionally, we provide scaling laws for relaxation of alloy surfaces in various kinetic regimes.